Multiply the following complex numbers: $({-1+4i}) \cdot ({5+2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+4i}) \cdot ({5+2i}) = $ $ ({-1} \cdot {5}) + ({-1} \cdot {2}i) + ({4}i \cdot {5}) + ({4}i \cdot {2}i) $ Then simplify the terms: $ (-5) + (-2i) + (20i) + (8 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -5 + (-2 + 20)i + 8i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -5 + (-2 + 20)i - 8 $ The result is simplified: $ (-5 - 8) + (18i) = -13+18i $